List of practice Questions

From a uniform circular disc of radius $R$ and mass $9 \,M$, a small disc of radius $\frac{R}{3}$ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is -
A body of mass $M$ and charge $q$ is connected to a spring of spring constant $k$. It is oscillating along x-direction about its equilibrium position, taken to be at $x = 0$, with an amplitude $A$. An electric field $E$ is applied along the x-direction. Which of the following statements is correct ?
If $x = \sqrt{2^{cosec^{-1} } t}$ and $y = \sqrt{2^{\sec^{-1}} t} (|t | \geq 1)$, then $\frac{dy}{dx}$ is equal to :
In a simultaneous throw of a pair of dice, the probability of getting a total more than 7 is
The negation of the statement "72 is divisible by 2 and 3" is
The potential energy of a simple harmonic oscillator of mass $2\, kg$ at its mean position is $5\, J.$ If its total energy is $9\, J$ and amplitude is $1\, cm$. then its time period is
Why is the heat evolved in neutralization of HF is highest
A flashlight has 10 batteries out of which 4 are dead. If 3 batteries are selected without replacement and tested, then the probability that all 3 are dead is
A bag contains 17 tickets numbered from 1 to 17. A ticket is draw at random, then another ticket is drawn at random, then another ticket is drawn without replacing the first one . The probability that both the tickets may show even numbers is
The number of the distinct real roots of the equation $\begin{vmatrix}\sin x&\cos x&\cos x\\ \cos x&\sin x&\cos x\\ \cos x&\cos x&\sin x\end{vmatrix} = 0 $ , in the interval $ - \frac{\pi}{4} \le x \le \frac{\pi}{4}$ is
Which one of the following group is nutritionally essential amino acids?
During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
From a collection of $20$ consecutive natural numbers, four are selected such that they are not consecutive. The number of such selections is
The movement of Pollen tube is:
The species, which has the bond order same as that of $F_2$, molecule is
Consider the following statements: Hardy Weinberg equilibrium is maintained in a population where (i) random mating is there (ii) there is no natural selection (iii) a population may gain or loose alleles Which of the statements given above is/are correct?
The antibody produced in allergic reaction is:
Dead burnt plaster is
Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
Identify the major product that is obtained on treatment of \(CH_3CH_2CH(F)CH_3\) with \(CH_3O^-/CH^3OH\) is
The ratio of the half-life time $ (t_{1/2}) $ , to the three quarter life-time, $ (t_{3/4}) $ , for a reaction that is second order
The value of magnetic quantum number of the last electron of " $ Na $ " is
If PUNE / GOA = 1 and CHENNAI / GOA = 1.5, then MUMBAI / PUNE = ?
When both trains meet, they are at the same point. Therefore, both trains are equidistant from Chennai.
The ratio of lowest energy in terms of wave numbers of Balmer and Lyman series of lines of atomic spectrum of hydrogen is